Diagonals AC and BD of trapezium ABCD in which AB || DC, intersect each other at O. The triangle which is equal in area to triangle BOC is

ΔDOC

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ΔADC

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ΔAOD

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ΔAOB

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Solution

The correct option is C ΔAOD

It can be observed that ΔDAC and ΔDBC lie on the same base DC and between the same parallels AB and CD.

∴ Area (ΔDAC) = Area (ΔDBC)

Subtracting the area of ΔDOC from both we get,

Area (ΔDAC) − Area (ΔDOC) = Area (ΔDBC) − Area (ΔDOC)

⇒ Area (ΔAOD) = Area (ΔBOC) (From the figure)

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